But with the Ex-Im Bank’s charter expiring May 31 and two House recesses between now and then, the number of legislative days provides only a short window for action.

Two industry sources close to the discussions say Cantor and Hoyer are close on substance and are working out the particulars of length of time and amount of money in loan authority. Still, the time frame is close enough that industry players are getting nervous.

“Discussions are ongoing,” Hoyer spokeswoman Katie Grant said.

The politics of the issue are sensitive. A solid bloc of conservatives are vowing to oppose the bank as unnecessary economic intervention by the government.

The bank “is a government subsidy to certain companies with influential friends favored by the federal government — picking private-sector winners and losers,” a who’s who of conservative leaders said in an April 17 memo.

A bipartisan deal between Cantor and Hoyer would provide any legislation with enough votes to bypass conservative opposition.

“We are working to formulate a bipartisan bill to reauthorize the Ex-Im Bank that includes needed reforms and accountability measures,” Cantor spokeswoman Laena Fallon recently said.

This has rankled the conservative outside groups that are lobbying fiercely against reauthorization.

“The Republican leadership still hasn’t learned the lessons of 2006, 2008 or Fannie and Freddie,” Club for Growth spokesman Barney Keller said.

However, not all conservatives are opposed to reauthorizing the bank. Rep. Blaine Luetkemeyer (Mo.), a member of the Republican Study Committee, is organizing a group of conservatives to express its support in a letter for reauthorization.

“I think a lot of folks don’t really understand what the Ex-Im Bank really does. I don’t think they understand the impact that it can have on our economy,” Luetkemeyer said.

There’s also a wrinkle on the legislative vehicle: Senate leaders oppose bringing up reauthorization as a stand-alone measure — they’d prefer it be attached to another bill. Cantor and Hoyer are discussing what it could be attached to.

A Senate Democratic leadership aide said Senate Majority Leader Harry Reid (D-Nev.) wants to try to attach the Ex-Im Bank reauthorization to a bill that will pass the House rather than passing it as stand-alone legislation. The aide said Reid has gone with the strategy because House Republican leaders do not want to bring up a stand-alone Ex-Im Bank bill because it might not pass with a majority of the majority.

The issue is also stoking an increasingly contentious lobbying fight, pitting Boeing Co., a leading bank beneficiary, against Delta Air Lines, which accuses the Ex-Im Bank of helping foreign airlines at the expense of U.S. carriers.

Although Cantor is seen as an ally of Delta, which has been fighting for restrictions on the bank, his effort to find common ground has drawn praise from the bank’s supporters.

Cantor is “the adult in the room,” one lobbyist involved in the fight recently said.

Pro-bank business groups, such as the U.S. Chamber of Commerce, which were caught off guard by assaults on the bank by the Club for Growth and its allies, have struck back hard.

The bank’s defenders have spotlighted Ex-Im Bank loans that benefited some of its leading critics, including Delta and Club for Growth President Chris Chocola, a businessman and former House Member from Indiana.

“This is a huge priority for the chamber and the business community,” said Christopher Wenk, senior director of international policy at the chamber, which has organized hundreds of meetings with lawmakers and their aides and is preparing its second pro-bank ad campaign. “We have a lot of companies, particularly small and medium-sized companies, that really rely on Ex-Im and the services it provides,” he said.

Typically reauthorized every four years, the bank is fast approaching its lending cap of $100 billion. At issue are the length of the bank’s charter and how high to raise the cap. Proposed lending limits have ranged from $113 billion to $140 billion, with talk of a compromise in the $130 billion range.